Laplace transforms of Heavyside functions

[logistics86]

Hi everyone,

I'm a long time lurker, first time poster and I was wondering if anyone could help me out with a little Laplace trouble i was having,

I am interested in solving the ODE

y' = -y+2*y*u(t-1)

where u is the heaviside function,

Any hints?

 

[g_edgar]

Hi everyone,

I'm a long time lurker, first time poster and I was wondering if anyone could help me out with a little Laplace trouble i was having,

I am interested in solving the ODE

y' = -y+2*y*u(t-1)

where u is the heaviside function,

Any hints?

What do you get for the Laplace transform of that ODE?

 

[HallsofIvy]

The problem is NOT the Heaviside function- that's easy. The problem is that there is no simple formula for the Laplace transform of the product of two functions. The Laplace transform simply is not useful for differential equations with variable coefficients.

 

[logistics86]

I thought that might be the case, can you suggest another technique I could look into to try and solve this sort of problem?

 

[logistics86]

problem solved, separation of variables will do the trick really easily.